Lesson Worksheet: Rearranging Formulas for Physical Quantities Physics • 9th Grade

In this worksheet, we will practice changing the subject of a formula and recognising valid rearrangements of combinations of formulas.

Q1:

One side of the formula 𝑣=𝑒+2π‘Žπ‘ οŠ¨οŠ¨ is π‘£οŠ¨. The formula is rearranged so that one side of the formula is equal to ο„ž(π‘£βˆ’π‘’)2π‘ οŠ¨οŠ¨. Which of the following is the other side of the formula equal to?

  • Aπ‘ŽοŠ¨
  • Bπ‘Ž
  • Cβˆ’π‘Ž
  • Dβˆšπ‘Ž

Q2:

Kinetic energy is given by the formula 𝐸=12π‘šπ‘£οŠ¨. The weight, π‘Š, of an object is π‘šπ‘”. Which of the following is a correct formula that has a subject equal to the ratio of the kinetic energy of an object to its weight?

  • AπΈπ‘Š=𝑔2π‘£οŠ¨
  • BπΈπ‘Š=2π‘£π‘”οŠ¨
  • CπΈπ‘Š=𝑣2π‘”οŠ¨
  • DπΈπ‘Š=2π‘”π‘£οŠ¨
  • EπΈπ‘Š=𝑔𝑣2

Q3:

The subject of the formula force = mass Γ— acceleration is force. Which of the following correctly shows the same formula with acceleration as the subject of the formula?

  • AAcceleration = massforce
  • BAcceleration = force Γ— mass
  • CAcceleration = forcemass

Q4:

The subject of the formula speeddistancetime= is speed. Which of the following correctly shows the same formula with time as the subject of the formula?

  • ATimedistancespeed=
  • BTimedistancespeed=Γ—
  • CTimespeeddistance=

Q5:

The subject of the formula accelerationfinalvelocityinitialvelocitytime=(βˆ’) is acceleration. Which of the following correctly shows the same formula with time as the subject of the formula?

  • ATimefinalvelocityinitialvelocityacceleration=(βˆ’)
  • BTimefinalvelocityinitialvelocityacceleration=(βˆ’)Γ—
  • CTimeaccelerationfinalvelocityinitialvelocity=(βˆ’)

Q6:

The momentum of an object is given by the formula momentum = mass Γ— velocity, expressed in symbols as 𝑝=π‘šπ‘£. The velocity of an object is given by the formula velocity = displacementtime, expressed in symbols as 𝑣=𝑠𝑑. Which of the following is a correct formula?

  • A𝑝𝑑=π‘šπ‘ 
  • B𝑝𝑑=𝑣𝑠
  • C𝑝𝑠=π‘šπ‘‘
  • D𝑝𝑣=π‘šπ‘ 
  • E𝑝𝑣=π‘šπ‘‘

Q7:

The subject of the formula accelerationfinalvelocityinitialvelocitytime=(βˆ’) is acceleration. Which of the following correctly shows the same formula with final velocity as the subject of the formula?

  • AFinalvelocityaccelerationtimeinitialvelocity=(Γ—)βˆ’
  • BFinalvelocityinitialvelocitytimeacceleration=(βˆ’)Γ—
  • CFinalvelocityaccelerationtimeinitialvelocity=(Γ—)+
  • DFinalvelocityinitialvelocitytimeacceleration=(Γ—)+
  • EFinalvelocityaccelerationinitialvelocitytime=(βˆ’)

Q8:

The subject of the formula for the volume of a cube, volume = sidelength, is volume. Which of the following correctly shows the same formula with side length as the subject of the formula?

  • ASidelength = οŽ’ο„volume
  • BSidelength = √volume
  • CSidelength = 1volume

Q9:

Gravitational potential energy is given by the formula 𝐸=π‘šπ‘”β„Ž, where 𝐸 is the energy, π‘š is the mass, 𝑔 is the acceleration due to gravity, and β„Ž is the height. Acceleration is given by the formula acceleration = changeinvelocitytime, written in symbols as π‘Ž=Δ𝑣𝑑. Which of the following is a correct formula?

  • Aβ„Ž=π‘šΞ”π‘£π‘‘πΈ
  • Bβ„Ž=πΈπ‘šπ‘‘Ξ”π‘£
  • Cβ„Ž=πΈΞ”π‘£π‘‘π‘š
  • Dβ„Ž=πΈπ‘‘π‘šΞ”π‘£
  • Eβ„Ž=Ξ”π‘£π‘‘πΈπ‘š

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